Abstract: This paper contains new results for helping to understand financial crises. First, we present a new model for obtaining the probability of equity crises within one year in advance, and we test it. Second and separately, various markets already in crises appear quantitatively related to a theory of nonlinear diffusion called the Reggeon Field Theory calculated years ago. Details are in a longer companion paper.

The time dynamics of the origins of crises are commonly pictured by bubbles growing and collapsing. Our dynamic model, the “CEEC (Critical Exponent Earthquake Crisis) Model”, has these features , and can provide early warning equity crisis signals to help prevent losses. The CEEC Model uses concepts of “critical exponents” from physics plus a qualitative analogy from earthquakes to describe the build-up of bubbles (increase of “frictional stress”) with subsequent crises from bubble collapses (“earthquakes”) . The only inputs to the CEEC model for an equity index are equity index returns.

Tests comparing the CEEC model to data yield encouraging results, much better than chance. Here are results from running the model as the user would have run it in the past:

• In 69% of the tests for which the model indicated a crisis in the short term (within one year), a crisis was in fact observed within one year. • 31% of actual crises were missed by the model within one year before the crisis.

We also analyze various markets already in crisis (equity, FX, commodities, rates, bonds). We find behavior numerically consistent with a theoretical result with no free parameters for the general theory of nonlinear diffusion in physics, generalizing standard Brownian motion, the Reggeon Field Theory RFT. An anomalous RFT critical exponent translated into finance language is around 0.3, and this number qualitatively describes the average behavior of markets in crisis.

This 0.3 RFT anomalous variance exponent is perhaps the first number calculated in advance since the Gaussian Brownian diffusion variance exponent (1.0) used in standard finance, without numerically fitting anything.

The attached presentation discusses Stressed VAR, a practical market risk measure that merges stress testing with VAR, using a familiar and theoretically consistent framework. Stressed VAR contains jump/tail effects using fat-tail Gaussian volatilities, stressed correlations that model turbulent market collective behavior, and a high confidence level. Estimates can be included for liquidity penalties, idiosyncratic risks, and time scales roughly incorporating dynamic trading effects. The presentation includes parameter estimation and application as well as theory.

The presentation also briefly discusses the Volatility of Component VAR.